The former paper takes a method of Higson [1]} that appeared also in Higson–Lafforgue–Skandalis [2]} and removed the group theory aspects to a large degree. The main concept they introduced, the notion of an asymptotically faithful covering sequence, is defined in Section . This is used there to construct lifting maps at the level of the Roe algebra - giving us the so called “Higson trace” (first constructed in [1]}). This notion of lifting is exploited to obtain the representation theory results of Section  that we apply in the setting of lacunary hyperbolic groups.
